@inbook{d7e6dedf249e4dc4877c35ed80142c27,

title = "Weak brill-noether for rational surfaces",

abstract = "A moduli space of sheaves satisfies weak Brill-Noether if the general sheaf in the moduli space has no cohomology. G{\"o}ttsche and Hirschowitz prove that on P2 every moduli space of Gieseker semistable sheaves of rank at least two and Euler characteristic zero satisfies weak Brill-Noether. In this paper, we give sufficient conditions for weak Brill-Noether to hold on rational surfaces. We completely characterize Chern characters on Hirzebruch surfaces for which weak Brill-Noether holds. We also prove that on a del Pezzo surface of degree at least 4 weak Brill-Noether holds if the first Chern class is nef.",

author = "Izzet Coskun and Jack Huizenga",

note = "Funding Information: 2010 Mathematics Subject Classification. Primary 14J60, 14J26; Secondary 14D20, 14F05. Key words and phrases. Moduli spaces of sheaves, Brill-Noether theory, rational surfaces, Hirzebruch and del Pezzo surfaces. During the preparation of this article the first author was partially supported by the NSF CAREER grant DMS-0950951535 and NSF grant DMS-1500031, and the second author was partially supported by a National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS-1204066 and an NSA Young Investigator Grant H98230-16-1-0306. Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",

year = "2018",

doi = "10.1090/conm/712/14343",

language = "English (US)",

series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

pages = "81--104",

booktitle = "Contemporary Mathematics",

address = "United States",

}